Answer:
The length of the rod for the condition on the question to be met is 
Explanation:
The Diagram for this question is gotten from the first uploaded image
From the question we are told that
The mass of the rod is 
The mass of each small bodies is 
The moment of inertia of the three-body system with respect to the described axis is 
The length of the rod is L
Generally the moment of inertia of this three-body system with respect to the described axis can be mathematically represented as
Where 
is the moment of inertia of the rod about the describe axis which is mathematically represented as
And 
the moment of inertia of the two small bodies which (from the diagram can be assumed as two small spheres) can be mathematically represented as
![I_m = m * [\frac{L} {2} ]^2 = m* \frac{L^2}{4}](https://tex.z-dn.net/?f=I_m%20%20%3D%20%20%20m%20%2A%20%5B%5Cfrac%7BL%7D%20%7B2%7D%20%5D%5E2%20%3D%20%20m%2A%20%20%5Cfrac%7BL%5E2%7D%7B4%7D)
Thus 
Hence
=> ![I = [\frac{M}{12} + \frac{m}{2}] L^2](https://tex.z-dn.net/?f=I%20%20%3D%20%20%20%20%5B%5Cfrac%7BM%7D%7B12%7D%20%20%2B%20%5Cfrac%7Bm%7D%7B2%7D%5D%20L%5E2)
substituting vales we have
![0.929 = [\frac{3.41}{12} + \frac{0.249}{2}] L^2](https://tex.z-dn.net/?f=0.929%20%20%20%3D%20%20%20%20%5B%5Cfrac%7B3.41%7D%7B12%7D%20%20%2B%20%5Cfrac%7B0.249%7D%7B2%7D%5D%20L%5E2)
The force of gravity is equal to the mass times centripetal acceleration.
Fg = m v^2 / r
The force of gravity is defined by Newton's law of universal gravitation as:
Fg = mMG / r^2
Therefore:
mMG / r^2 = m v^2 / r
MG / r = v^2
v increases as r decreases. So the planet with the smallest orbit (closest to the sun) will have the highest orbital velocity. Of the four options, that's Mercury.
Answer:
increase speed, decrease speed, and change direction
Explanation:
Answer:
The charge-to-mass ratio of the particle is 5.7 × 10⁵ C/kg
Explanation:
From the formulae
F = qvB and F = mv²/r
Where F is Force
q is charge
v is speed
B is magnetic field strength
m is mass
and r is radius
Then,
qvB = mv²/r
qB = mv/r
We can write that
q/m = v/rB ---- (1)
Also
From Electric force formula
F = Eq
Where E is the electric field
and magnetic force formula
F = Bqv
Since, electric force = magnetic force
Then, Eq = Bqv
E = Bv
∴ v = E/B
Substitute v = E/B into equation (1)
q/m = (E/B)/rB
∴ q/m = E/rB²
(NOTE: q/m is the charge to mass ratio)
From the question,
E = 3.10 ×10³ N/C
r = 4.20 cm = 0.0420 m
B = 0.360 T
Hence,
q/m = 3.10 ×10³ / 0.0420 × (0.360)²
q/m = 569517.9306 C/kg
q/m = 5.7 × 10⁵ C/kg
Hence, the charge-to-mass ratio of the particle is 5.7 × 10⁵ C/kg.
